no. 9
Mathematical Analysis/Mathematical Economics
An extension of Brouwer's fixed point theorem allowing discontinuities
[Une extension du théorème du point fixe de Brouwer autorisant des discontinuités]

Présenté par : Pierre-Louis Lions

Bich, Philippe1
1 CEREMADE, Université de Paris Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
Comptes Rendus. Mathématique, Tome 338 (2004) no. 9, pp. 673-678.

Nous étendons dans cet article le théorème du point fixe de Brouwer – qui dit que toute fonction f continue de B dans B (une boule fermée de ℝ n ) admet un point fixe – en autorisant un certain type de discontinuité de f sur un ensemble éventuellement infini, et appliquons cette extension à la théorie de l'équilibre général en économie.

In this article, we extend Brouwer's fixed point theorem – which states that every continuous mapping f:B→B (a closed ball of ℝ n ) must have a fixed point – by allowing discontinuities of f, and we apply this extension to equilibrium theory in Economics.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.03.001
Bich, Philippe 1

1 CEREMADE, Université de Paris Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France 
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Bich, Philippe. An extension of Brouwer's fixed point theorem allowing discontinuities. Comptes Rendus. Mathématique, Tome 338 (2004) no. 9, pp. 673-678. doi : 10.1016/j.crma.2004.03.001. http://www.numdam.org/articles/10.1016/j.crma.2004.03.001/

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